课程名称︰古典电力学上 课程性质︰必修 课程教师︰朱国瑞 开课学院：理学院 开课系所︰物理所 考试日期（年月日）︰10/12/10 考试时限（分钟）：120min 是否需发放奖励金：Yes （如未明确表示，则不予发放） 试题 : 1 Answer “yes” or “no” to the following statements (no explanation is is required ) Notations follow Jackson . Two point for each correct answer ; no penalty for wrong answers .(24%) (1) Eq (1.13) gives exactly the same information as Eq (1.15) (2) ε_0 E^2 (x)and qδ(x-x_0)φ(x) have the same dimension (3) Legendre function of the first kind P_ν (x)diverges at x=1 unless ν an integer . (4) Bessel function of the first kind J_n (x) is a monotonically increasing function of x , where n is a positive integer . (5) Electric polarization and electric dipole moment do not have the same dimension (6) The polarization charge density (ρ_pol=-▽˙P)is only a convenient definition It does not represent real charges . (7) φ(x) in (4.84) does not include contribution from the polarization charge (8) Eq(4.89) can be applied to a linear , anisotropic , and nonuniform dielectric medium . (9) In magnetostatics , ∫_νJd^3x=0for an arbitrary volume (ν) of integration (10) Eq(5.22) gives exactly the same information as Eq(5.24) (11) Eq(5.147) is derived from Eq(5.146) under the assumption that the volume of integration is infinity . (12) A static magnetic field can penetrate through a conductor with μ=μ_0 as if there were no conductor present . 2 A point charge q is brought from infinity to a distance d from an infinite grounded , plane conductor . If the induced surface charge on the conductor is now "frozen" in place and the point charge is removed , what is the energy in the remaining electric field ?(15%) 3 A conducting sphere of radius a with net charge Q on its surface is placed in a uniform electric field E_0 (e_z ) ? . Use the method of expansion to find φ outside the sphere . 4 (a) Refer to the mechanism of dipole formation discussed in Sec4.6 . Find the energy required to induce a dipole on an atomic or molecular charge e by an electric field E ? .(8%) (b) From W=1/2 ∫E。D d^3x [(4.89)] , we deduce that , in a dielectric , the energy density due to the presence of E ? is w=1/2 E ??D ? . Derive this relation using the result in part (a) .(8%) 5 Explain why the derivation of the magnetic field energy in Jackson Sec 5.16 is valid only when the current J ? is established at an infinistesimally small rate. (10%) 6 A copper rod of length L is pivoted at one end and rotates with constant angular velocity ω about an axis perpendicular to its length . A uniform magnetic induction B ? is applied parallel to the axis of rotation . Calculate the potential difference between the ends of the rod ? (15%) 贴完了~ --

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